Answer:
the linear regression line for the given data is: y = 0.24x + 2.49
Step-by-step explanation:
To find the linear regression line for the given data, we need to first calculate the mean of x, the mean of y, the sum of squares of x, the sum of squares of y, and the sum of cross-products of x and y.
Using these values, we can then calculate the slope and y-intercept of the regression line.
First, we calculate the mean of x and y:
mean of x = (4 + 6 + 12 + 14 + 17) / 5 = 10.6
mean of y = (2 + 5 + 2 + 8 + 9) / 5 = 5.2
Next, we calculate the sum of squares of x and y:
sum of squares of x = (4 - 10.6)^2 + (6 - 10.6)^2 + (12 - 10.6)^2 + (14 - 10.6)^2 + (17 - 10.6)^2 = 240.4
sum of squares of y = (2 - 5.2)^2 + (5 - 5.2)^2 + (2 - 5.2)^2 + (8 - 5.2)^2 + (9 - 5.2)^2 = 44.8
Finally, we calculate the sum of cross-products of x and y:
sum of cross-products of x and y = (4 - 10.6)(2 - 5.2) + (6 - 10.6)(5 - 5.2) + (12 - 10.6)(2 - 5.2) + (14 - 10.6)(8 - 5.2) + (17 - 10.6)(9 - 5.2) = 56.8
Using these values, we can calculate the slope of the regression line:
slope = sum of cross-products of x and y / sum of squares of x = 56.8 / 240.4 = 0.236
Next, we can calculate the y-intercept of the regression line:
y-intercept = mean of y - slope * mean of x = 5.2 - 0.236 * 10.6 = 2.488
Therefore, the linear regression line for the given data is:
y = 0.24x + 2.49
Note: The slope and y-intercept have been rounded to two decimal places, as per the instructions.
Determine the length of x in the triangle. Give your answer to two decimal places. Show the steps, please.
Answer:
35.09 units
Step-by-step explanation:
This is a right-angled triangle where:
Hypotenuse = x units
With respect to angle 20°:
Opposite = 12 units
Use trigonometric function sinФ to solve for x:
sinФ = [tex]\frac{Opposite}{Hypotenuse}[/tex]
∴sin20° = [tex]\frac{12}{x}[/tex]
Cross-multiplication is applied:
[tex](x)(sin20) = 12[/tex]
x has to be isolated and made the subject of the equation:
∴[tex]x = \frac{12}{sin20}[/tex]
x = 35.09 units (Rounded to 2 decimal places)
Answer:
The length of x is 35.09 units to two decimal places.
Step-by-step explanation:
In the given right triangle, we have been given the length of the side opposite the angle and need to find the length of the hypotenuse.
To find the value of x, use the sine trigonometric ratio.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
Substitute θ = 20°, O = 12 and H = x into the ratio and solve for x:
[tex]\implies \sin 20^{\circ}=\dfrac{12}{x}[/tex]
[tex]\implies x=\dfrac{12}{\sin 20^{\circ}}[/tex]
[tex]\implies x=35.085652...[/tex]
[tex]\implies x=35.09\; \sf (2\;d.p.)[/tex]
Therefore, the length of x is 35.09 units to two decimal places.
Which transformations would take Figure A to Figure B?
select all that are equal to 6^4 (6^5)
The density of the object is equal to the quotient of its mass, m, and its volume, v . An object has a density of 8 grams per liter and a volume of 16 liters. What is its mass in grams
Answer:
the formula for density is:
density = mass/volume
We know that the density of the object is 8 grams per liter, and its volume is 16 liters. We can use this information to solve for the mass:
density = mass/volume
8 g/L = mass/16 L
To solve for the mass, we can cross-multiply and simplify:
8 g/L * 16 L = mass
128 g = mass
Therefore, the mass of the object is 128 grams.
The price of an item has dropped to $44 today. Yesterday it was $80. Find the percentage decrease
Answer:
To find the percentage decrease, we need to find the difference between the original price and the new price, divide that difference by the original price, and then multiply by 100 to get the percentage.
The difference between the original price and the new price is:
80 - 44 = 36
To find the percentage decrease, we divide this difference by the original price:
36 / 80 = 0.45
Finally, we multiply by 100 to get the percentage:
0.45 * 100 = 45%
Therefore, the percentage decrease from $80 to $44 is 45%.
Answer: The percentage decrease is 45%.
Step-by-step explanation:
Percentage decrease = [tex](\frac{Oringinal Value-NewValue}{Oringinal Value} )*100[/tex]
= [tex](\frac{80-44}{80} )*100[/tex]
= 45%
HOW TO TAKE OUT HCF BY PRIME FACTORISATION
Therefore , Highest Common Factor (HCF) of two or more numbers by prime factorisation method can be done by following below given steps
What is an unitary method?This generally recognized ease, preexisting variables, and any necessary elements from the initial Diocesan customizable query may all be used to complete the job. Consequently, you might be given another chance to use the item. Otherwise, important impacts on algorithmic statistics will vanish.
Here,
To find the Highest Common Factor (HCF) of two or more numbers by prime factorisation method, follow these steps:
Express each number as a product of prime factors.
Identify the common prime factors among the numbers.
Take the product of the common prime factors. This product will be the HCF of the given numbers.
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Please help will mark Brainly
Answer:
[tex]\mathrm{D.\:\:\:f(x) = 2x^2 - 2x - 4; A = 8}[/tex]
Step-by-step explanation:
The formula for the area of a rectangle is A = l x w, where A is the area, l is the length, and w is the width. In this case, the length is 2x - 4 units and the width is x + 1 units. Therefore, the function that models the area of the rectangle is:
f(x) = (2x - 4)(x + 1)
f(x) = 2x^2 - 2x - 4
Therefore, option D is the correct answer.
To find the area when x = 3, we substitute x = 3 into the function:
f(3) = 2(3)^2 - 2(3) - 4
f(3) = 18 - 6 - 4
f(3) = 8
Therefore, when x = 3, the area of the rectangle is 8 square units.
1.A trader sold some goods for #5184 and lost 4%. Find the total cost price of the goods?
Therefore, the total cost price of the goods is #5400.
What is cost price?Cost price refers to the amount of money that is spent by a business or individual to acquire or produce a product or service. It includes all the costs involved in the production or acquisition of the product or service, such as raw materials, labor costs, transportation costs, and other expenses. The cost price is usually used as a starting point for calculating the selling price of a product or service and is an important factor in determining the profitability of a business.
by the question.
Let's assume the cost price of the goods to be "x".
According to the problem, the trader sold the goods at a price of #5184 and incurred a loss of 4%.
we know that,
selling price = cost price - loss
Substituting the given values in the above formula, we get:
#5184 = x - 0.04x
Simplifying the equation, we get:
#5184 = 0.96x
Dividing both sides by 0.96, we get:
x = #5400
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For the numbers 683 and 2329 round each number to the nearest hundred, then find the product of the rounded numbers
Answer:
1,610,000
Step-by-step explanation:
To round to the nearest hundred, we need to go to the hundreds place. In 683, we can round this to the nearest hundred by using this rule:
5 or more, let it sore
4 or less, let it rest
683 rounded to the nearest hundred is 700
2329 rounded to the nearest hundred is 2300
Now we just need to multiply both of them to get the product
[tex]2300\times 700=1,610,000[/tex]
How many times will Sarah have to deposit $300 every six months into her account at 4.5%
compounded semi-annually to save $10 000.00?
25.15
20.82
15.75
1458.90
With 4.5% compounded semi-annually, Sarah will need to make installments for roughly 20.82 years in order to save $10,000. Hence, 20.82 is the answer.
Is every two years or semiannually?
Simply said, semiannual refers to events that occur twice a year. A couple might commemorate their nuptials each two years, a corporation might hold workplace celebrations each two years, as well as a family might go on vacation each two years. Every two years, something that happens twice a year does.
We can utilize the calculation again for future value of an annuity to resolve this issue:
FV = P × ((1 + r/n) - 1) / (r/n)
Where:
FV = Future value
P = Periodic payment
r = Annual interest rate
n = Compounding cycles per year, number
t = Number of years
In this instance, Sarah plans to deposit $300 each six months in order to save $10,000. She will so be required to make two payments each year. P thus equals $300, n equals 2, r equals 0.045 (decimalized 4.5%), and FV equals $10,000. The number of years, t, needs to be solved for.
$10,000 = $300 × ((1 + 0.045/2) - 1) / (0.045/2)
When we simplify this equation, we obtain:
20 = (1 + 0.0225) - 1
21 = (1 + 0.0225)
Using both sides' natural logarithms:
ln(21) = ln((1 + 0.0225))
ln(21) = 2×t × ln(1 + 0.0225)
t = ln(21) / (2 × ln(1 + 0.0225))
t = 20.82
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Latasha and Nathan both leave the coffee shop at the same time, but in opposite directions. If Nathan travels 8mph faster than Latasha and after 9 hours they are 288 miles apart , how fast is each traveling
Answer:
Let's use the formula:
distance = rate × time
Let's assume Latasha's rate of travel as "r". Then, Nathan's rate of travel would be "r + 8".
For Latasha:
distance = r × 9
For Nathan:
distance = (r + 8) × 9
According to the problem, the combined distance they traveled is 288 miles. So:
r × 9 + (r + 8) × 9 = 288
Simplifying the equation:
18r + 72 = 288
18r = 216
r = 12
So, Latasha's rate of travel is 12 mph, and Nathan's rate of travel is 20 mph (12 + 8).
Therefore, Latasha is traveling at 12 mph and Nathan is traveling at 20 mph.
Lost-time accidents occur in a company at a mean rate of 0.4 per day. What is the probability that the number of lost-time accidents occurring over a period of 9 days will be at least 4 ? Round your answer to four decimal places.
The prοbability οf that the number οf lοst-time accidents οccurring οver a periοd οf 9 days will be at least 4 is 0.3975.
What is prοbability?Prοbability is a way οf calculating hοw likely sοmething is tο happen. It is difficult tο prοvide a cοmplete predictiοn fοr many events. Using it, we can οnly fοrecast the prοbability, οr likelihοοd, οf an event οccurring. The prοbability might be between 0 and 1, where 0 denοtes an impοssibility and 1 denοtes a certainty.
We can use here Pοisson distribution with λ=0.4 * 8=3.2
[tex]P[X\geq 4]=1-P[X < 4][/tex]
[tex]=1-{P[X=0] + P[X=1] + P[X=2] +P[X=3] =1-{0.0408+ 0.1304+ 0.2087 + 0.2226} =0.3975[/tex]
Where,
[tex]P[X=0]=\frac{e^{-3.2}(3.2)^0}{0!} = 0.0408[/tex]
[tex]P[X=1]=\frac{e^{-3.2}(3.2)^1}{1!} = 0.1304[/tex]
[tex]P[X=2]=\frac{e^{-3.2}(3.2)^2}{2!} = 0.2087[/tex]
[tex]P[X=3]=\frac{e^{-3.2}(3.2)^3}{3!} = 0.2226[/tex]
Hence the prοbability of that the number of lost-time accidents οccurring over a period of 9 days will be at least 4 is 0.3975.
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Suppose the demand and supply of beer are modeled by the two following functions:
Q = -57P + 364
Q = 25P + 26
What is the equilibrium quantity of beer? Round your answer to two places after the decimal point (0.01).
Therefore , the solution of the given problem of unitary method comes out to be $240 which will cover the cost of the new motorbike.
What is an unitary method?The task can be completed by multiplying the data gathered using this type of nanosection along with two individuals variable who utilized the unilateral strategy. In essence, this signifies that perhaps the designated entity is defined or the colour of both mass production is skipped whenever a wanted item occurs. For forty pens, a variable charge of Inr ($1.01) could have been required.
Here,
The quantity supplied and the quantity requested are equal when there is equilibrium. As a result, we can equalise the two formulae and find the equilibrium quantity:
=> -57P + 364 = 25P + 26
=> 82P = 338
=> P = 4.12
We can use either equation to determine the equilibrium amount now that we know the equilibrium price. Use the supply calculation as an example:
=> Q = 25P + 26
=> Q = 25(4.12) + 26
=> Q = 129.5
So, rounded to two decimal places, the equilibrium amount of beer is roughly 129.5.
=> $60 + $180 = $240
which will cover the cost of the new motorbike.
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PLEASE HELP!!!
Consider this equation. cos ( θ ) = 8/9 If θ is an angle in quadrant IV, what is the value of tan ( θ ) ?
let's keep in mind that in the IV Quadrant, the cosine is positive whilst the sine is negative, so hmm
[tex]\cos(\theta )=\cfrac{\stackrel{adjacent}{8}}{\underset{hypotenuse}{9}} \qquad \textit{let's find the \underline{opposite side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{9}\\ a=\stackrel{adjacent}{8}\\ o=opposite \end{cases}[/tex]
[tex]o=\pm\sqrt{ 9^2 - 8^2}\implies o=\pm\sqrt{ 81 - 64 } \implies o=\pm\sqrt{ 17 }\implies \stackrel{ IV~Quadrant }{o=-\sqrt{17}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \tan(\theta )=\cfrac{\stackrel{opposite}{-\sqrt{17}}}{\underset{adjacent}{8}}~\hfill[/tex]
To find the value of tan(θ) when cos(θ) = 8/9 and θ is in the fourth quadrant, use the relation sin^2(θ) = 1 - cos^2(θ) to determine sin(θ). Then compute tan(θ) = sin(θ) / cos(θ). The result will be negative
Explanation:Given the equation cos(θ) = 8/9 in the fourth quadrant of the Cartesian plane, you are required to determine the value of tan(θ). In the fourth quadrant, cosine values are positive, and sine values are negative. You can use the relation sin^2(θ) = 1 - cos^2(θ). So, sin(θ) would be -sqrt(1 - (8/9)^2). The tangent of an angle in any quadrant can be found by taking the ratio of the sine to the cosine, i.e., tan(θ) = sin(θ) / cos(θ). Substitute the values of sine and cosine to find the value of tan(θ). It turns out that tan(θ) will be negative in the fourth quadrant.
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A rectangular pyramid has a height of 5 units and a volume of 50 units3. Shannon states that a rectangular prism with the same base area and height has a volume that is three times the size of the given rectangular pyramid. Which statement explains whether Shannon is correct?
A rectangular prism in which BA = 10 and h = 5 has a volume of 150 units3; therefore, Shannon is correct
A rectangular prism in which BA = 30 and h = 5 has a volume of 150 units3; therefore, Shannon is correct
A rectangular prism in which BA = 10 and h = 5 has a volume of 50 units3; therefore, Shannon is incorrect
A rectangular prism in which BA = 30 and h = 5 has a volume of 50 units3; therefore, Shannon is incorrect
Answer:
B (A rectangular prism in which BA = 30 and h = 5 has a volume of 150 units3; therefore, Shannon is correct)
Step-by-step explanation:
I took the test!
The solution is,: A rectangular prism in which BA = 30 and h = 5 has a volume of 150 units^3; therefore, Shannon is correct
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
step 1
Find the area of the base of the rectangular pyramid
we know that:
The volume of the rectangular pyramid is equal to:
V = 1/3 * bh
where
B is the area of the base
H is the height of the pyramid
we have
V= 50
h = 5
substitute and solve for B
we get,
b= 30
step 2
Find the volume of the rectangular prism with the same base area and height
we know that
The volume of the rectangular prism is equal to
V = bh
we have
b = 30
h = 5
substitute
V = 30 * 5 = 150 unit^3
therefore
The rectangular prism has a volume that is three times the size of the given rectangular pyramid. Shannon is correct
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345.61489 rounded to the nearest ten- thousandth
Answer: 345.6149
Step-by-step explanation:
Answer:
345.6149
Step-by-step explanation:
15. Many people swimming in a pool experience pain in their ears if they dive to the
bottom. Why is this?
A. Pressure increases as the depth of the water column above them increases.
B. The area of the pool is wider where it's deeper.
C. Pressure decreases as the depth of the water column above them increases.
D. The vapor pressure at the surface is removed.
Answer:
The answer is Ahope this helps
I want you to help me solve the variable equations of questions 3
Answer:
[tex]\huge\boxed{\sf x = -24}[/tex]
Step-by-step explanation:
Given equation:[tex]\displaystyle -\frac{1}{2} x - 4 =8\\\\Add \ 4 \ to \ both \ sides\\\\-\frac{1}{2} x = 8+4\\\\-\frac{1}{2} x = 12\\\\Multiply \ both \ sides \ by \ -2\\\\-\frac{1}{2} x \times \ -2 = 12 \times -2\\\\\boxed{x = -24}\\\\\rule[225]{225}{2}[/tex]
Answer:
[tex]\boxed{\mathtt{1) \ x=4}}[/tex]
[tex]\boxed{\mathtt{2) \ x=2}}[/tex]
[tex]\boxed{\mathtt{3) \ x=-24}}[/tex]
Step-by-step explanation:
[tex]\textsf{For these problems, we are asked to solve for x in each equation.}[/tex]
[tex]\textsf{We should use similar steps for each of them.}[/tex]
[tex]\large\underline{\textsf{For Number 1:}}[/tex]
[tex]\textsf{We should first begin by adding 2 to both sides of the equation.}[/tex]
[tex]\mathtt{8x=32}[/tex]
[tex]\textsf{Now, divide by 8.}[/tex]
[tex]\boxed{\mathtt{1) \ x=4}}[/tex]
[tex]\large\underline{\textsf{For Number 2:}}[/tex]
[tex]\textsf{Let's begin by subtracting 5 from both sides of the equation.}[/tex]
[tex]\mathtt{-x=-2}[/tex]
[tex]\textsf{Now, divide by -1.}[/tex]
[tex]\boxed{\mathtt{2) \ x=2}}[/tex]
[tex]\large\underline{\textsf{For Number 3:}}[/tex]
[tex]\textsf{Beginning Number 3, let's multiply by -2 to both sides of the equation.}[/tex]
[tex]\mathtt{x+8=-16}[/tex]
[tex]\textsf{Now, subtract 8 from both sides of the equation.}[/tex]
[tex]\boxed{\mathtt{3) \ x=-24}}[/tex]
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equations that can be used to solve for y, the length of the room are: y² - 5y - 750 = 0 , (y - 30)(y + 25) = 0 , y(y - 5) + 750 = 0
Define the term equation?An equation is a mathematical statement that asserts the equality of two expressions, often with variables and constants.
To solve for y, we can use the same equation we used for x, since y represents the length of the room. Therefore, the equation we can use to solve for y is:
y² - 5y - 750 = 0
This equation can be factored as (y - 30)(y + 25) = 0, which gives us two solutions: y = 30 or y = -25. However, since the length of a room cannot be negative, the only valid solution is y = 30.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
The expression for the area of the shaded region in its simplest form is x² + 23x + 49.
What is the area of the rectangle?
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
The shaded area is the difference of the areas of the rectangle and the square.
Rectangle:
A₁ = (x + 10)(2x + 5) = 2x² + 5x + 20x + 50 = 2x² + 25x + 50
Square:
A₂ = (x + 1)² = x² + 2x + 1
Shaded region:
A₁ - A₂ = 2x² + 25x + 50 - (x² + 2x + 1)
= 2x² + 25x + 50 - x² - 2x - 1
= x² + 23x + 49
Hence, the expression for the area of the shaded region in its simplest form is x² + 23x + 49.
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Complete question:
Enter your answer and show all the steps that you use to solve this problem in the space provided.
A rectangle is shown with length x plus 10 and width 2 x plus 5. The inside of the rectangle is shaded other than an unshaded square with length x plus 1 and width x plus 1.
Write an expression for the area of the shaded region in its simplest form. Show all of your steps.
I need help with please
Answer:
C
Step-by-step explanation:
You want to identify the set of ordered pairs corresponding to the given pattern definitions.
Start atThe x-pattern starts at 2.
The y-pattern starts at 0.
The first (x, y) ordered pair is (2, 0). This matches answer choice C.
__
Additional comment
The x-rule tells you the sequence is ...
2, 2+6 = 8, 8+6 = 14, 14+6 = 20 . . . . . {2, 8, 14, 20}
The y-rule tells you the sequence is ...
0, 0+5 = 5, 5+5 = 10, 10+5 = 15 . . . . . {0, 5, 10, 15}
Then the (x, y) pairs are ...
(2, 0), (8, 5), (14, 10), (20, 15)
Note that when X and Y are the variables involved, we conventionally use the ordered pair (x, y). When other variables are involved, the ordered pair may be different, not always alphabetic order.
Generally, the independent variable is listed first. Here, neither depends on the other, so that criterion does not apply. Listing X first here is also suggested by the fact that the X pattern rule is defined first.
Which statements are true? Select each correct answer. Responses 15m3−6m=3m(5m2−6m) 15 m cubed minus 6 m equals 3 m left parenthesis 5 m squared minus 6 m right parenthesis 40m6−4=4(10m6−1) 40 m begn power 6 end power minus 4 equals 4 left parenthesis 10 begin power 6 end power minus 1 right parenthesis 32m4+12m3=4m3(8m+3) 32 m begin power 4 end power plus 12 m cubed equals 4 m cubed left parenthesis 8 m plus 3 right parenthesis 6m2+18m=6m2(1+3m)
The true statement are:
A. 15m3-6m=3m(5m2-6m),
B. 40m6-4=4(10m6-1),
C. 6m2+18m=6m2(1+3m),
What are the true statement?15m3-6m=3m(5m2-6m) - This is true. Factoring out 3m from the terms on the left side gives 3m(5m2 - 2), which matches the right side.40m6-4=4(10m6-1) - This is true. Distributing 4 on the right side gives 4(10m6) - 4, which simplifies to the left side.6m2+18m=6m2(1+3m) - This is true. Factoring out 6m2 from the terms on the left side gives 6m2(1 + 3m), which matches the right side.32m4+12m3(8m+3) - This is not an equation or inequality, so it cannot be true or false.Therefore the correct option is A, B, C.
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The correct question is:
Which statements are true
15m3-6m=3m(5m2-6m),
40m6-4=4(10m6-1),
6m2+18m=6m2(1+3m),
32m4+12m3(8m+3)
Divide 1/20 divide by 5 enter your answer in the box as a fraction in simplest form
Answer:
honestly don't know but you got this bro {=•=}
Drag and drop 3 coordinates that satisfy the system above
Y<-2x + 4
2x-4y ≥ 3
The three coordinates that satisfy the system of inequalities include the following:
(0, -2)
(-7, - 5)
(-2, -8).
What is an ordered pair?In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.
By critically observing the graph of the given system of inequalities y < -2x + 4 and 2x - 4y ≥ 3, the three required solutions that satisfies it include following;
Ordered pair = (0, -2).
Ordered pair = (-7, - 5).
Ordered pair = (-2, -8).
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Please I need help with this question
!!! Please quickly need an answer!!!!
Car A and car B set off from the same point to travel the same journey. Car A sets off three minutes before car B. If car A travels at 60 km/h and car B travels at 70 km/h, how many kilometres from the starting point will the two cars draw level?
The two cars will draw level at a distance of 12 kilometers from the starting point, taking their speed and into consideration, as further explained below.
How to find the distanceSince both cars are traveling towards the same destination, the distance between them will decrease over time until they draw level. Let's call the distance between the starting point and the meeting point "d" kilometers. We can use the formula:
distance = rate × time
Since car A has a three-minute head start, car B will have to travel for three minutes less than car A. Let's call the time it takes for car B to catch up to car A "t" hours. Then:
time for car A = t + 3/60 hours
time for car B = t hours
We want to find the distance between the starting point and the meeting point, which is the same for both cars. So we can set up an equation based on their distances:
distance traveled by car A = distance traveled by car B
(rate for car A) × (time for car A) = (rate for car B) × (time for car B)
60 × (t + 3/60) = 70 × t
3 = 10t
t = 3/10 hours
Now that we know the time it takes for car B to catch up to car A, we can use either car's rate and time to find the distance between the starting point and the meeting point. Let's use car A's rate and time:
distance = rate × time
distance = 60 × (t + 3/60)
distance = 60 × (3/10 + 1/20)
distance = 60 × (4/20)
distance = 12 kilometers
Therefore, the two cars will meet 12 kilometers from the starting point.
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1, a 36 foot tree cast an 18 foot Shadow at the
Same time that a mail box carts a 4 foot shadow
how tall is the mail box
Answer:
We can use the concept of proportions to solve this problem. We know that the ratio of the height of the tree to the length of its shadow is the same as the ratio of the height of the mailbox to the length of its shadow.
Let's call the height of the mailbox "x". Then, we can set up the proportion:
height of tree / length of tree's shadow = height of mailbox / length of mailbox's shadow
Plugging in the values we know, we get:
36 / 18 = x / 4
Simplifying the left side of the equation, we get:
2 = x / 4
To solve for x, we can multiply both sides of the equation by 4:
8 = x
Therefore, the mailbox is 8 feet tall.
Step-by-step explanation:
Answer:
Height of mail box = 8 ft
Step-by-step explanation:
Given information,
→ 18 ft shadow is formed by a 36 ft tree.
→ A mail box casts 4 foot shadow.
Now we have to,
→ Find the height of the mail box.
Let us assume that,
→ Height of mail box = h
Forming the equation,
→ 36/18 = h/4
Then the value of h will be,
→ 36/18 = h/4
→ h/4 = 36/18
→ h/4 = 2
→ h = 2 × 4
→ [ h = 8 ft ]
Hence, the value of h is 8.
Joanna went school supply shopping. She spent $23.89 on notebooks and pencils. Notebooks cost $1.87 each and pencils cost $1.08 each. She bought a total of 17 notebooks and pencils. How many of each did she buy?
Answer: She
bought a total of 5 notebooks and 13 pencils.
Step-by-step explanation:
A steel rod of mass 25kg is melted down to create ball bearings of radius 4mm. One kilogram of this steel has a volume of 150[tex]cm^3[/tex]. How many ball bearings could be made from this steel rod?
Therefore, approximately 110,294 ball bearings of radius 4mm can be made from the steel rod.
What is volume?Volume is the amount of space that a three-dimensional object occupies. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet. The volume of an object can be calculated by multiplying its length, width, and height, or by using a specific formula for the shape of the object, such as the formula for the volume of a sphere, cylinder, or cone. Volume is an important concept in mathematics, physics, engineering, and many other fields, and it is used to describe the size and shape of objects, as well as their capacity, density, and other properties.
Here,
To solve this problem, we need to determine the total volume of the steel rod and then calculate how many ball bearings of radius 4mm can be made from this volume. First, we need to calculate the volume of the steel rod. We are given that one kilogram of the steel has a volume of 150 cm³. Therefore, the total volume of the steel rod is:
25 kg * 150 cm³/kg = 3750 cm³
Next, we need to calculate the volume of one ball bearing of radius 4mm. The formula for the volume of a sphere is:
V = (4/3)πr³
Substituting r = 4mm = 0.4cm, we get:
V = (4/3)π(0.4)³ = 0.034 cm³ (rounded to three decimal places)
To find the number of ball bearings that can be made from the steel rod, we divide the total volume of the steel rod by the volume of one ball bearing:
3750 cm³ / 0.034 cm³ ≈ 110,294
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5. Find the time in which the loan of N3,900 at the rate of 5% yields N585=
6 What time will the simple interest N70,000 at the rate of 7% be used
for a loan of N20,000.00=
7.If N300.00 amount to N390 at the rate of 3%. Find the time.=
8.The simple interest on N5600.00 in 1 year is N80.00, find the rate percent per annum=
9.What year will N5100 yield an interest of N170.00 at the rate of 2 1/2 per annum=
10.What rate per annum will N4,600 yield an interest of N230.00 for 2 years=
11. What time will N8100 yield an interest of N729 at the rate of 9% per annum=
12.Report from the bank says the interest on N2300 is N23.00 for 2 years find the rate of interest per annum.=
Answer:
5. To find the time in which the loan of N3,900 at the rate of 5% yields N585, we can use the formula for simple interest:
I = P * r * t
where I is the interest, P is the principal (the amount borrowed), r is the interest rate (as a decimal), and t is the time (in years).
Plugging in the given values, we get:
585 = 3900 * 0.05 * t
Solving for t, we get:
t = 3 years
Therefore, it will take 3 years for the loan to yield N585 in interest.
6. To find the time it will take for the simple interest on N70,000 at the rate of 7% to be N20,000, we can again use the formula for simple interest:
I = P * r * t
Plugging in the given values, we get:
20000 = 70000 * 0.07 * t
Solving for t, we get:
t = 4 years
Therefore, it will take 4 years for the simple interest on N70,000 at the rate of 7% to be N20,000.
7. To find the time it takes for N300 to amount to N390 at the rate of 3%, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
where A is the final amount, P is the principal (the initial amount), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).
Plugging in the given values, we get:
390 = 300 * (1 + 0.03/1)^(1*t)
Simplifying, we get:
1.3^t = 1.3
Taking the logarithm of both sides, we get:
t = log(1.3) / log(1.3)
t ≈ 1.82
Therefore, it takes approximately 1.82 years for N300 to amount to N390 at the rate of 3%.
8. To find the rate percent per annum for a simple interest of N80 on N5600 in 1 year, we can use the formula for simple interest:
I = P * r * t
Plugging in the given values, we get:
80 = 5600 * r * 1
Solving for r, we get:
r = 0.0143 or 1.43%
Therefore, the rate percent per annum is 1.43%.
9. To find the year in which N5100 will yield an interest of N170 at the rate of 2 1/2 per annum, we can use the formula for simple interest:
I = P * r * t
Plugging in the given values, we get:
170 = 5100 * 0.025 * t
Solving for t, we get:
t = 2/3 years
Since the question asks for the year, we need to add 2/3 years to the current year. Assuming the current year is 2021, we get:
2021 + 2/3 ≈ 2022.67
Therefore, N5100 will yield an interest of N170 at the rate of 2 1/2 per annum in the year 2022.
10. To find the rate per annum at which N4,600 will yield an interest of N230 for 2 years, we can again use the formula for simple interest:
I = P * r * t
Plugging in the given values, we get:
230 = 4600 * r * 2
Solving for r, we get:
r = 0.025 or 2.5%
Therefore, the rate per annum is 2.5%.
11. To find the time it takes for N8100 to yield an interest of N729 at the rate of 9% per annum, we can use the formula for simple interest:
I = P * r * t
Plugging in the given values, we get:
729 = 8100 * 0.09 * t
Solving for t, we get:
t = 1 year
Therefore, it takes 1 year for N8100 to yield an interest of N729 at the rate of 9% per annum.
12. To find the rate of interest per annum for an interest of N23 on N2300 for 2 years, we can use the formula for simple interest:
I = P * r * t
Plugging in the given values, we get:
23 = 2300 * r * 2
Solving for r, we get:
r = 0.005 or 0.5%
Therefore, the rate of interest per annum is 0.5%.